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Modern cyber-physical systems-of-systems (CPSoS) operate in complex systems-of-systems that must seamlessly work together to control safety- or mission-critical functions. Linear Temporal Logic (LTL) and Mission-time Linear Temporal logic (MLTL) intuitively express CPSoS requirements for automated system verification and validation. However, both LTL and MLTL presume that all signals populating the variables in a formula are sampled over the same rate and type (e.g., time or distance), and agree on a standard “time” step. Formal verification of cyber-physical systems-of-systems needs validate-able requirements expressed over (sub-)system signals of different types, such as signals sampled at different timescales, distances, or levels of abstraction, expressed in the same formula. Previous works developed more expressive logics to account for types (e.g., timescales) by sacrificing the intuitive simplicity of LTL. However, a legible direct one-to-one correspondence between a verbal and formal specification will ease validation, reduce bugs, increase productivity, and linearize the workflow from a project’s conception to actualization. Validation includes both transparency for human interpretation, and tractability for automated reasoning, as CPSoS often run on resource-limited embedded systems. To address these challenges, we introduced Mission-time Linear Temporal Logic Multi-type (Hariharan et al., Numerical Software Verification Workshop, 2022), a logic building on MLTL. MLTLM enables writing formal requirements over finite input signals (e.g., sensor signals and local computations) of different types, while maintaining the same simplicity as LTL and MLTL. Furthermore, MLTLM maintains a direct correspondence between a verbal requirement and its corresponding formal specification. Additionally, reasoning a formal specification in the intended type (e.g., hourly for an hourly rate, and per second for a seconds rate) will use significantly less memory in resource-constrained hardware. This article extends the previous work with (1) many illustrated examples on types (e.g., time and space) expressed in the same specification, (2) proofs omitted for space in the workshop version, (3) proofs of succinctness of MLTLM compared to MLTL, and (4) a minimal translation to MLTL of optimal length.
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Mission-time LTL (MLTL) Formula Validation Via Regular Expressions
Mission-time Linear Temporal Logic (MLTL) represents the most practical fragment of Metric Temporal Logic; MLTL resembles the popular logic Linear Temporal Logic (LTL) with finite closed-interval integer bounds on the temporal operators. Increasingly, many tools reason over MLTL specifications, yet these tools are useful only when system designers can validate the input specifications. We design an automated characterization of the structure of the computations that satisfy a given MLTL formula using regular expressions. We prove soundness and completeness of our structure. We also give an algorithm for automated MLTL formula validation and analyze its complexity both theoretically and experimentally. Additionally, we generate a test suite using control flow diagrams to robustly test our implementation and release an open-source tool with a user-friendly graphical interface. The result of our contributions are improvements to existing algorithms for MLTL analysis, and are applicable to many other tools for automated, efficient MLTL formula validation. Our updated tool may be found at https://temporallogic.org/research/WEST.
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- Award ID(s):
- 2038903
- PAR ID:
- 10564704
- Publisher / Repository:
- Springer
- Date Published:
- ISBN:
- 978-3-031-47704-1
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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